We introduce new approaches for forecasting IBNR (Incurred But Not Reported) frequencies by leveraging individual claims data, which includes accident date, reporting delay, and possibly additional features for every reported claim. A key element of our proposal involves computing development factors, which may be influenced by both the accident date and other features. These development factors serve as the basis for predictions. While we assume close to continuous observations of accident date and reporting delay, the development factors can be expressed at any level of granularity, such as months, quarters, or year and predictions across different granularity levels exhibit coherence. The calculation of development factors relies on the estimation of a hazard function in reverse development time, and we present three distinct methods for estimating this function: the Cox proportional hazard model, a feed-forward neural network, and xgboost (eXtreme gradient boosting). In all three cases, estimation is based on the same partial likelihood that accommodates left truncation and ties in the data. While the first case is a semi-parametric model that assumes in parts a log linear structure, the two machine learning approaches only assume that the baseline and the other factors are multiplicatively separable. Through an extensive simulation study and real-world data application, our approach demonstrates promising results. This paper comes with an accompanying R-package, $\texttt{ReSurv}$, which can be accessed at \url{https://github.com/edhofman/ReSurv}

翻译：我们提出了一种利用个体理赔数据预测IBNR（已发生未报告）频率的新方法，数据涵盖每起已报告理赔的事故日期、报告延迟及可能的附加特征。本方案的关键要素在于计算发展因子，该因子可能同时受事故日期及其他特征影响。发展因子作为预测基础；尽管我们假设事故日期和报告延迟接近连续观测，但发展因子可按月、季度或年等任意粒度层级表达，且不同粒度层级的预测具有一致性。发展因子的计算依赖于逆向发展时间风险函数的估计，我们提出了三种估计方法：Cox比例风险模型、前馈神经网络及xgboost（极端梯度提升）。三种方法的估计均基于同一部分似然函数，可处理数据中的左截断与结值问题。第一种方法为半参数模型，其部分结构假设呈对数线性；而两种机器学习方法仅假设基线与其他因子满足乘法可分离性。通过大量模拟研究与实际数据应用，本方法展现出良好表现。本文附有R语言包$\texttt{ReSurv}$，可通过\url{https://github.com/edhofman/ReSurv}获取。